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#

Approximated solution for non-linear fits with normal errors

Linearity implies that the arguments of the exponential
of the integrand in Eq. (28) contains only
first and second powers of , and then the integrals
has a closed solution. Though this is not true in general,
the linear case teaches us how to get an approximated
solution of the problem. We can take first order expansions
of
around each

The difference
in Eq. (28),
that was indeed equal to
in the general case,
using the linear approximation becomes

i.e.
we have the following replacements in Eqs. (28)-(30):

The approximated equivalent of
Eq. (30) is then

where the unusual symbol `
' stands for
`approximately proportional to'.

** Next:** Extra variability of the
** Up:** Fits, and especially linear
** Previous:** Linear fit with normal
Giulio D'Agostini
2005-11-21